Hi there, clark. Changing Alerts (Email) within QuickBooks Time is unavailable. However, you can add a user using your employee's work address. Let's get into the details.
When an email field in QuickBooks Time shows the QuickBooks logo and says Imported from QuickBooks on hover, that user’s profile is being synced from the Intuit/QuickBooks side, not from QuickBooks Time itself. Because of this, QuickBooks Time treats that email as read‑only, so you can’t override it for alerts just in the Time product.
Since changing Alerts (Email) within QuickBooks Time is unavailable, I recommend adding a user to QuickBooks Online (QBO) using their work email for the time approval and letting them continue to use their workforce account using their personal email.
You can use the photo below as a reference:

After the user accepts the invite, go to Classic QuickBooks Time, then click the QuickBooks Payroll icon and hit Import. This will sync all the changes from QuickBooks Online to QuickBooks Time.

Once you're done, edit the role of the newly invited user to Payroll Manager. Here's how:
1. Go to My Team, then click the three dots beside the invited user.

2. Click on Edit, then go to Permissions.
3. Select Payroll Manager and Save.

I also recommend changing the role of your previous employee to Custom or Worker. This will ensure that only the newly invited user can approve time off.

Come back to this post if you have other questions or concerns.